Characters of odd degree

Abstract

We prove the McKay conjecture on characters of odd degree. A major step in the proof is the verification of the inductive McKay condition for groups of Lie type and primes $\ell$ such that a Sylow $\ell$-subgroup or its maximal normal abelian subgroup is contained in a maximally split torus by means of a new equivariant version of Harish-Chandra induction. Specifics of characters of odd degree, namely, that most of them lie in the principal Harish-Chandra series, then allow us to deduce from it the McKay conjecture for the prime $2$, hence for characters of odd degree.

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    @ARTICLE{Sp13, mrkey = {3100954},
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    @ARTICLE{Spaeth2, mrkey = {2602390},
      number = {9},
      issn = {0021-8693},
      author = {Sp{ä}th, Britta},
      mrclass = {20C33 (20C20 20G05 20G40)},
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    @ARTICLE{Sp12, mrkey = {2966987},
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      issn = {0024-6093},
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      journal = {Bull. Lond. Math. Soc.},
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      issn = {0020-9910},
      author = {Springer, T. A.},
      mrclass = {20H15},
      doi = {10.1007/BF01390173},
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    @ARTICLE{Tits, mrkey = {0206117},
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Authors

Gunter Malle

FB Mathematik, TU Kaiserslautern, Kaisers\-lautern, Germany

Britta Späth

Universität Wuppertal, School of Mathematics and Natural Sciences, Wuppertal, Germany